The voltage of a car battery can be somewhere between 11.5 and 14 or so volts, disconnected or with the engine off. During cranking it can drop below that range and while charging it might be above that range. Auto systems are also loaded with noise and voltage spikes so instantaneous voltage can be much higher.
If you leave the 7812 in the circuit it will only function to reduce the high range of the voltage. As I understand it there is a voltage drop or loss that normally requires the input voltage to the 7812 to be several volts above the desired regulated output voltage. If your circuit really does need 12 volts you might just get 12 volts out of the 7812 when the system voltage is at 14 volts or above, otherwise it will fall short. I am not sure if this will affect your circuit.
To what degree the 7812 will suppress voltage spikes is unknown to me. You might add a 15 volt or higher zener across the input and give it a try. I don't know that an undervoltage condition would do any harm though the data (reading) might appear good and yet be unreliable. Some electronic devices will only function reliably with the nice, smooth, noise free power of a battery so best to experiment.
If your device does need 12 volts you can get closer to it with a low dropout regulator if the current requirements are less than the particular regulator. If your device will function reliably at let's say 10 volts you might use an LM317 ( or better yet a low dropout regulator) to supply a steadier voltage more of the time. A switched mode regulator would ultimately the the best as long as the output were properly filtered.
The water analogy is the best. In case it didn't sink in just consider that small, low wattage, mains (120 or 220 vac) light bulbs are in your light fixtures connected to the same source (mains) as other high current loads. Until the fuse or circuit breaker opens there can be 10,000 or much more available amps (short circuit) yet things function just fine.